Course detail

(Ordered Sets and Lattices

FSI-9UMSAcad. year: 2016/2017Summer semesterNot applicable.. year of study1  credit

Students will get acquainted with basic concepts and results of the theory of ordered sets and lattices used in many branches of mathematics and in other disciplines, e.g., in informatics.

Learning outcomes of the course unit

Not applicable.

Prerequisites

Not applicable.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Steve Roman, Lattices and ordered sets, Springer, New York 2008. (EN)
Jan Kopka, Svazy a Booleovy algebry, Univerzita J.E. Purkyně v Ústaí nad Labem, 1991 (CS)

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Language of instruction

Czech, English

Work placements

Not applicable.

Aims

Not applicable.

Type of course unit

 

Lecture

20 hours, optionally

Teacher / Lecturer

Syllabus

1. Basic concepts of the theory of ordered sets
2. Axiom of Choice and equivalent theorems
3. Duality and monotonne maps
4. Down-sets and up-sets, ascending and descending chain conditions
5. Well ordered sets and ordinal numbers
6. Cardinal numbers, cardinal and ordinal arithmetic
7. Closure operators on ordered sets
8. Ideals and filters
9. Modular and distributive lattices
10. Boolean lattices